Color with falloff | Animation nodes 2.1 in blender 2.81a
You can make use of the "Viewport Color" property of each object, since this property can be accessed in any shader. 

See my answer here for more information : https://blender.stackexchange.com/a/163699/86891

In your animation node tree, you need to add an "Object Attribute Output" set to "color" :



Edit :

As of V 2.1.7, thanks to 3DSinghVFX there is a node specifically for this : The object color output.



Then access it in your shader :



These two objects share the same shader, but I am modifying the left one's color in my animation nodes tree :



In order to change each individual object's color, use this setup :



Don't forget to tweak the "Evaluate Fallof" node to output a list instead of just one value. You need to click on the button on the right of the "location" field in this node. Notice how it is blue tinted.
Result :